Question

BD and AC are chords that intersect at point Y. A circle is shown. Chords B C and A C intersect at point Y. The length of B Y is 3, the length of Y D is 8, the length of A Y is x, and the length of Y C is 6. What is the length of line segment AY? 2 units 3 units 4 units 6 units

Answer 1

Answer:

4 units

Step-by-step explanation:

we know that

The Intersecting Chord Theorem states that:  When two chords intersect each other inside a circle, then the products of their segments are equal.

do

In this problem

$(BY)(YD)=(AY)(YC)$

substitute the given values

$(3)(8)=(x)(6)$

solve for x

$24=6x\\x=24/6\\x=4\ units$

therefore

The length of segment AY is 4 units

Answer 2

Answer:

AY = 4 units

Step-by-step explanation:

The image is attached below.

We have to find the value of AY (or x).

We need the intersecting chord theorem to solve this easily.

The intersecting chord theorem tells us that the product of line segment of each chord are equal.

From the figure, we can state:

BY * YD = AY * YC

Thus, we can write:

$BY * YD = AY * YC\\3*8=x*6\\24=6x\\x=\frac{24}{6}\\x=4$

Hence,

AY = 4 units